It is shown that the transition process to BEC phase of excitons can be manifested as non-monotonic kinetics of photoluminescence decay. This decay looks as a series of subsequent peaks resulting from superradiance phenomenon. We show that decay of PL of certain InAs-GaSb coupled quantum wells having, for instance, in average 5 ground state excitons per island may demonstrate up to 5 consecutive maximums followed by exponential decay. This dependence may be considered as a manifestation of transition to the Bose condensate phase. The radiation kinetics of such a system is a generalization of the known two-level Dicke superradiance to an ensemble of multilevel systems.